Related papers: A Class of Quasi-Stationary Regular Line Elements …
In this paper, the Eddington-Finkelstein transformation is used as an illustration of how the problem of singularities or infinities can be removed by application of nonstandard analysis to the Schwarzschild line element (metric). The…
Guided by a Hamiltonian treatment of spherically symmetric geometry, we find a remarkably simple -- stationary, but not static -- form for the line element of Schwarzschild (and Reissner-Nordstrom) geometry. The line element continues…
A general geometrical scheme is presented for the construction of novel classical gravity theories whose solutions obey two-sided bounds on the sectional curvatures along certain subvarieties of the Grassmannian of two-planes. The…
The paper deals with a special kind of problems that appear in solutions of Einstein's field equations for extended bodies: many structure-dependent terms appear in intermediate calculations that cancel exactly in virtue of the local…
Spherically symmetric solutions in Brans-Dicke theory of relativity with zero coupling constant, $\omega=0$, are derived in the Schwarzschild line-element. The solutions are obtained from a cubic transition equation with one small…
In this paper we analyze the spacetime geometry due to a Schwarzschild object having uniform accelerated motion. In the beginning, we investigate the gravitational field due to a uniformly moving Schwarzschild object and obtain the…
The Schwarzschild geometry is investigated within the context of effective-field-theory models of gravity. Starting from its harmonic-coordinate expression, we derive the metric in standard coordinates by keeping the leading one-loop…
This work is a purely syntactic geometric exploration of some few elements, which are our axioms, that in last instance it is the set of differential equations whose solutions give the geodesic lines of the Schwarzschild spacetime. We…
Since Schwarzshild discovered the point-mass solution to Einstein's equations that bears his name, many equivalent forms of the metric have been catalogued. Using an elementary coordinate transformation, we derive the most general form for…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
The Schwarzschild-deSitter metric is the known solution of Einstein field equations with cosmological constant term for vacuum spherically symmetric space around a point mass M. Recently it has been reported that in a $Lamda$-dominant world…
Using canonical (Schrodinger) quantization of spherically symetric gravitational dust systems, we find the quasi-classical (coherent) state, |\alpha^{(s)}>, that corresponds to the classical Schwarzschild solution. We calculate the…
A rigidity result for a class of compact generalized quasi-Einstein manifolds with constant scalar curvature is obtained. Moreover, under some geometric assumptions, the rigidity for the noncompact case is also proved. Considering non…
In this article, we study the geometry of compact quasi-Einstein manifolds with boundary. We establish sharp boundary estimates for compact quasi-Einstein manifolds with boundary that improve some previous results. Moreover, we obtain a…
In this paper, we solved the Einstein's field equation and obtained a line element for static, ellipsoidal objects characterized by the linear eccentricity ($\eta$) instead of quadrupole parameter ($q$). This line element recovers the…
In a previous paper we have considered the Regge-Wheeler equation for fields of spin $s=0$, $1$ or $2$ on the Schwarzschild spacetime in coordinates that are regular at the horizon. In particular, we have constructed in…
We prove (Theorem 1.1.) that a class of quasi-Einstein structures on closed manifolds must admit a Killing vector field. This extends the rigidity theorem obtained in \cite{DL23} for the extremal black hole horizons and completes the…
We develop a geometric and explicit construction principle that generates classes of Poincare-Einstein manifolds, and more generally almost Einstein manifolds. Almost Einstein manifolds satisfy a generalisation of the Einstein condition;…
We consider a broad class of static, spherically symmetric generalized Schwarzschild-like solutions with multiple non-interacting anisotropic fluid sources and derive the coordinate transformation from Schwarzschild-like (curvature) to…
A reformulation of the Schwarzschild solution of the linearised Einstein field equations in post-Riemannian Finsler spacetime is derived. The solution is constructed in three stages: the exterior solution, the event-horizon solution and the…